Information on Result #546854
There is no linear OA(3204, 223, F3, 135) (dual of [223, 19, 136]-code), because residual code would yield OA(369, 87, S3, 45), but
- the linear programming bound shows that M ≥ 60 677445 989371 388018 255266 871453 026648 079313 / 55230 725056 > 369 [i]
Mode: Bound (linear).
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(3205, 224, F3, 136) (dual of [224, 19, 137]-code) | [i] | Truncation | |
| 2 | No linear OA(3206, 225, F3, 137) (dual of [225, 19, 138]-code) | [i] | ||
| 3 | No linear OOA(3205, 223, F3, 2, 136) (dual of [(223, 2), 241, 137]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3206, 223, F3, 2, 137) (dual of [(223, 2), 240, 138]-NRT-code) | [i] | ||
| 5 | No linear OOA(3204, 223, F3, 2, 135) (dual of [(223, 2), 242, 136]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3204, 223, F3, 3, 135) (dual of [(223, 3), 465, 136]-NRT-code) | [i] | ||
| 7 | No linear OOA(3204, 223, F3, 4, 135) (dual of [(223, 4), 688, 136]-NRT-code) | [i] | ||
| 8 | No linear OOA(3204, 223, F3, 5, 135) (dual of [(223, 5), 911, 136]-NRT-code) | [i] | ||
| 9 | No digital (69, 204, 223)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |